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Applied Maths MCQ

Model Paper 10 · CBSE STD 12 Science (CBSE - English Medium). 18 questions.

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18 questions · timed · auto-graded

MCQ 11 Mark
An orderly set of data arranged in accordance with their time of occurrence is called:
  • ✓
    Time Series
  • B
    Harmonic Series
  • C
    Geometric Series
  • D
    Arithmetic Series
Answer
Correct option: A.
Time Series
(a) Time Series
Explanation: The organized series of data on the basis of any measure of time is called Time series.
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MCQ 21 Mark
$\int x^3 \log x d x$ is equal to
  • A
    $\frac{x^4}{8}\left(\log x-\frac{4}{x^2}\right)+C$
  • ✓
    $\frac{x^4}{16}(4 \log x-1)+C$
  • C
    $\frac{x^4}{16}(4 \log x+1)+C$
  • D
    $\frac{x^4 \log x}{4}+C$
Answer
Correct option: B.
$\frac{x^4}{16}(4 \log x-1)+C$
(b) $\frac{x^4}{16}(4 \log x-1)+C$
Explanation: $\int \frac{x_{ II }^3}{3} \log x d x=\log x \int x^3 d x-\int\left\{\frac{d}{d x} \log x \int x^3 d x\right\} d x$
$\begin{array}{l}=\log x \cdot \frac{x^4}{4}-\int \frac{1}{x} \cdot \frac{x^4}{4} d x=\frac{x^4}{4} \log x-\frac{x^4}{16}+ C \\ =\frac{x^4}{16}(4 \log x-1)+ C \end{array}$
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MCQ 31 Mark
In a school, a random sample of 145 students is taken to check whether a student's average calory intake is 1500 or not. The collected data of average calories intake of sample students is presented in a frequency distribution which is called a
  • ✓
    Sampling distribution
  • B
    Parameter
  • C
    Population sampling
  • D
    Statistics
Answer
Correct option: A.
Sampling distribution
(a) Sampling distribution
Explanation: Sampling distribution
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MCQ 41 Mark
If $\frac{1}{2}\left(\frac{3}{5} x+4\right) \geq \frac{1}{3}(x-6), x \in R$, then
  • A
    $x \in(-\infty, 120)$
  • ✓
    $x \in(-\infty, 120]$
  • C
    $x \in[120, \infty)$
  • D
    $x \in(120, \infty)$
Answer
Correct option: B.
$x \in(-\infty, 120]$
(b) $x \in(-\infty, 120]$
Explanation:$x \in(-\infty, 120]$
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MCQ 51 Mark
The optimal value of the objective function is attained at the points
  • ✓
    given by corner points of the feasible region
  • B
    given by intersection of inequations with xaxis only
  • C
    given by intersection of inequations with yaxis only
  • D
    given by intersection of inequations with the axes only
Answer
Correct option: A.
given by corner points of the feasible region
(a) given by corner points of the feasible region
Explanation: It is known that the optimal value of the objective function is attained at any of the corner points.
Thus, the optimal value of the objective function is attained at the points given by corner points of the feasible region.
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MCQ 61 Mark
A pipe can fill an empty cistern in 5 hours. A leak develops in the cistern due to which full cistern is emptied in 30 hours. With the leak, the cistern can be filled in
  • A
    12 hours
  • B
    8 hours
  • ✓
    6 hours
  • D
    10 hours
Answer
Correct option: C.
6 hours
(c) 6 hours
Explanation: Tap A can fill the cistern in 5 hour and leak L can empty the cistern in 30 hours.
So $\frac{1}{5}-\frac{1}{30}=\frac{6-1}{30}=\frac{5}{3}$ Part can be filled in 1 hours
$\therefore$ total time to fill the cistern
$=\frac{30}{5}=6$ hours
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MCQ 71 Mark
If $|x+3| \geq 10$, then
  • ✓
    $x \in(-\infty,-13] \cup[7, \infty)$
  • B
    $x \in(-13,7]$
  • C
    $x \in(-\infty,-13) \cup(7, \infty)$
  • D
    $x \in(-13,7)$
Answer
Correct option: A.
$x \in(-\infty,-13] \cup[7, \infty)$
(a) $x \in(-\infty,-13] \cup[7, \infty)$
Explanation: $|x+3| \geq 10$
$\begin{array}{l} x +3 \leq-10 \text { and } x +3 \geq 10 \\ \Rightarrow x \leq-13 \text { and } x \geq 7 \\ \Rightarrow x \in(-\infty,-13][7, \infty)\end{array}$
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MCQ 81 Mark
In what ratio must water be mixed with milk to gain $16 \frac{2}{3} \%$ on selling the mixture at cost price?
  • ✓
    1:6
  • B
    4:3
  • C
    6:1
  • D
    2:3
Answer
Correct option: A.
1:6
(a) 1:6
Explanation: Let C.P. of 1 litre milk be ₹ 1
S.P. of 1 litre of mixture = ₹ 1, Gain = $\frac{50}{3} \%$
$\therefore$ C.P. of 1 litre of mixture = $100 \times \frac{3}{350} \times 1=\frac{6}{7}$
By the rule of allegation, we have
Image
$\therefore$ Ratio of water and milk = $\frac{1}{7}: \frac{6}{7}=1: 6$
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MCQ 91 Mark
The order of the differential equation $2 x ^2 \frac{d^2 y}{d x^2}-3 \frac{d y}{d x}+ y =0$, is:
  • ✓
    2
  • B
    0
  • C
    1
  • D
    3
Answer
Correct option: A.
2
(a) 2
Explanation: It is given that equation is $2 x ^2 \frac{d^2 y}{d x^2}-3 \frac{d y}{d x}+ y =0$
We can see that the highest order derivative present in the given differential equation is $\frac{d^2 y}{d x^2}$ Thus, its order is two.
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MCQ 101 Mark
A boat goes downstream at u km/hr and upstream at v km/hr. The speed of the boat in still water, in km/hr is
  • A
    (u - v)
  • B
    u + v
  • C
    $\frac{1}{2}( u - v )$
  • ✓
    $\frac{1}{2}( u + v )$
Answer
Correct option: D.
$\frac{1}{2}( u + v )$
(d) $\frac{1}{2}( u + v )$
Explanation: Let the boat and stream speed be x km/hr and y km/hr
downstream speed = x + y
u = x + y ...(i)
upstream speed = x - y
v = x - y ...(ii)
(i) + (ii)
2x = u + v
$x =\frac{u+v}{2}$
$\therefore$ speed of boat in still water = $\frac{u+v}{2} km / hr$
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MCQ 111 Mark
The integrating factor of the differential equation (x log x)$\frac{d y}{d x}+ y =2$ log x, is given by:
  • A
    x
  • B
    log (log x)
  • C
    $x^2$
  • ✓
    log x
Answer
Correct option: D.
log x
(d) log x
Explanation: Given equation can be written as$\frac{d y}{d x}+\frac{y}{x \log x}=\frac{2}{x}$
Therefore, I.F. =$e^{\int \frac{1}{x \log x} d x}= e ^{\log (\log x)}=\log x$
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MCQ 121 Mark
If X is a Poisson variable such that P(X = 1) = 2P(X = 2), then P(X = 0) is
  • A
    $e ^2$
  • B
    e
  • C
    1
  • ✓
    $\frac{1}{e}$
Answer
Correct option: D.
$\frac{1}{e}$
(d) $\frac{1}{e}$
Explanation: Given P(X = 1) = 2 P(X = 2)
$\Rightarrow \frac{\lambda^1 e^{-\lambda}}{1!}=2 \times \frac{\lambda^2 \cdot e^{-\lambda}}{2!}$
$\Rightarrow \lambda=\lambda^2 \Rightarrow \lambda=0,1 \Rightarrow \lambda=1$
Now, P(X = 0)$=\frac{\lambda^0 \cdot e^{-\lambda}}{0!}=e^{-1}=\frac{1}{e}$
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MCQ 131 Mark
The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is
  • A
    ${ }^5 C_1(0.7)(0.3)^4$
  • ✓
    ${ }^5 C _4(0.7)^4(0.3)$
  • C
    $(0.7)^4(0.3)$
  • D
    ${ }^5 C _4(0.7)(0.3)^4$
Answer
Correct option: B.
${ }^5 C _4(0.7)^4(0.3)$
(b) ${ }^5 C _4(0.7)^4(0.3)$
Explanation: Here, $\bar{p}=0.3 \Rightarrow p =0.7$ and $q =0.3, n =5$ and $r =4$
$\therefore$ Required probability $={ }^5 C _4(0.7)^4(0.3)$
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MCQ 141 Mark
If x is real, the minimum value of$x^2-8 x+17$ is
  • A
    0
  • ✓
    1
  • C
    2
  • D
    -1
Answer
Correct option: B.
1
(b) 1
Explanation: Let $y=x^2-8 x+17=\left(x^2-2 \times 4 \times x+4^2\right)+1=(x-4)^2+1$
We know that if x is a real number then $x^2 \geq 0$
$\Rightarrow(x-4)^2 \geq 0$
Hence minimum value of y is 0 + 1 = 1
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MCQ 151 Mark
The maximum value of Z = 2x + 3y subject to the constraints: $x+y \leq 1,3 x+y \leq 4, x, y \geq 0$ is:
  • ✓
    5
  • B
    3
  • C
    4
  • D
    2
Answer
Correct option: A.
5
(a) 5
Explanation: 5
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MCQ 161 Mark
A certain sum of money amounts to ₹ 5832 in 2 years at 8% p.a. compound interest. The sum invested is
  • A
    ₹ 5280
  • B
    ₹ 5400
  • C
    ₹ 5200
  • ✓
    ₹ 5000
Answer
Correct option: D.
₹ 5000
(d) ₹ 5000
Explanation: Let sum invested be ₹ x, rate = 8%, time = 2 years
Amount = ₹ 5832
$\therefore 5832=x\left(1+\frac{8}{100}\right)^2$
$\Rightarrow 5832- x \times\left(\frac{27}{25}\right)^2$
$\Rightarrow x=\frac{5832 \times 25 \times 25}{27 \times 27}=5000$
$\therefore$ Sum invested = ₹ 5000
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MCQ 171 Mark
What does it mean that you calculate a 95% confidence interval?
  • ✓
    All of these
  • B
    The process you used will capture the true parameter 95% of the time in long run.
  • C
    You can be 95% confident that your interval will include the population parameter.
  • D
    You can be 5% confident that your interval will not include the population parameter.
Answer
Correct option: A.
All of these
(a) All of these
Explanation: All of these
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MCQ 181 Mark
If$\left[\begin{array}{cc}x+y & x+2 \\ 2 x-y & 16\end{array}\right]=\left[\begin{array}{cc}8 & 5 \\ 1 & 3 y+1\end{array}\right]$ , then the value of x and y are:
  • A
    x = 7, y = 2
  • B
    x = 5, y = 3
  • ✓
    x = 3, y = 5
  • D
    x = 2, y = 7
Answer
Correct option: C.
x = 3, y = 5
(c) x = 3, y = 5
Explanation: x = 3, y = 5
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MCQ - Applied Maths STD 12 Science Questions - Vidyadip